Solve for x, y, z

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3\left(y+2z\right)-z=7
Substitute y+2z for x in the equation 3x-z=7.
y=\frac{7}{3}-\frac{5}{3}z z=\frac{7}{3}+\frac{1}{3}y
Solve the second equation for y and the third equation for z.
z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right)
Substitute \frac{7}{3}-\frac{5}{3}z for y in the equation z=\frac{7}{3}+\frac{1}{3}y.
z=2
Solve z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right) for z.
y=\frac{7}{3}-\frac{5}{3}\times 2
Substitute 2 for z in the equation y=\frac{7}{3}-\frac{5}{3}z.
y=-1
Calculate y from y=\frac{7}{3}-\frac{5}{3}\times 2.
x=-1+2\times 2
Substitute -1 for y and 2 for z in the equation x=y+2z.
x=3
Calculate x from x=-1+2\times 2.
x=3 y=-1 z=2
The system is now solved.